To determine the length of the cable needed to support the volleyball net post, we can use the Pythagorean theorem. The setup forms a right triangle where:
- One leg is the vertical distance from the hook on the post to the court surface (4 ft).
- The other leg is the horizontal distance from the base of the post to the hook on the floor (3 ft).
- The hypotenuse will be the length of the cable we want to calculate.
Using the Pythagorean theorem:
\[ c^2 = a^2 + b^2 \]
where:
- \(a = 4\) ft (vertical leg),
- \(b = 3\) ft (horizontal leg),
- \(c\) is the length of the cable.
Substituting the values:
\[ c^2 = 4^2 + 3^2 \] \[ c^2 = 16 + 9 \] \[ c^2 = 25 \]
Now, taking the square root of both sides to find \(c\):
\[ c = \sqrt{25} = 5 \text{ ft} \]
Therefore, the length of the cable should be 5 feet.
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